Differential/Difference Equations

The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics, electrical, radio engineering, and vibrotechnics. This Special Issue includes 19 high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology. This Special Issue brought together mathematicians with physicists, engineers, as well as other scientists. Topics covered in this issue: Oscillation theory; Differential/difference equations; Partial differential equations; Dynamical systems; Fractional calculus; Delays; Mathematical modeling and oscillations

Forced Oscillations of Nonlinear Hyperbolic Equations with Functional Arguments via Riccati Method

By using integral averaging method and a generalized Riccati technique, sufficient conditions are established for the oscillation of solutions of forced nonlinear hyperbolic equations with functional arguments

Qualitative behaviour of solutions of the Goursat problem for hyperbolic differential equations

AbstractOscillation criteria and asymptotic behavior of solutions of characteristic initial-value problems have been extended to the Goursat problem

On the Zeros of the Solutions to Nonlinear Hyperbolic Equations with Delays

2002 Mathematics Subject Classification: Primary 35В05; Secondary 35L15We consider the nonlinear hyperbolic equation with delays uxy + λuxy(x - σ, у - τ) + c(x, у, u, ux, uy) = f(x, у) . We obtain sufficient conditions for oscillation of the solutions of problems of Goursat in the case, where λ>0.This work was partly supported by Grant MM-437 and Grant MM-516

Oscillation criteria for fractional impulsive hybrid partial differential equations

In this paper, we study the oscillatory behavior of the solutions of fractional-order nonlinear impulsive hybrid partial differential equations with the mixed boundary condition. By using the integral averaging method and the Riccati technique, we have obtained the oscillation criteria of all the solutions of the given system. An example is given to illustrate our main results

New developments in Functional and Fractional Differential Equations and in Lie Symmetry

Delay, difference, functional, fractional, and partial differential equations have many applications in science and engineering. In this Special Issue, 29 experts co-authored 10 papers dealing with these subjects. A summary of the main points of these papers follows:Several oscillation conditions for a first-order linear differential equation with non-monotone delay are established in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, whereas a sharp oscillation criterion using the notion of slowly varying functions is established in A Sharp Oscillation Criterion for a Linear Differential Equation with Variable Delay. The approximation of a linear autonomous differential equation with a small delay is considered in Approximation of a Linear Autonomous Differential Equation with Small Delay; the model of infection diseases by Marchuk is studied in Around the Model of Infection Disease: The Cauchy Matrix and Its Properties. Exact solutions to fractional-order Fokker–Planck equations are presented in New Exact Solutions and Conservation Laws to the Fractional-Order Fokker–Planck Equations, and a spectral collocation approach to solving a class of time-fractional stochastic heat equations driven by Brownian motion is constructed in A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise. A finite difference approximation method for a space fractional convection-diffusion model with variable coefficients is proposed in Finite Difference Approximation Method for a Space Fractional Convection–Diffusion Equation with Variable Coefficients; existence results for a nonlinear fractional difference equation with delay and impulses are established in On Nonlinear Fractional Difference Equation with Delay and Impulses. A complete Noether symmetry analysis of a generalized coupled Lane–Emden–Klein–Gordon–Fock system with central symmetry is provided in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, and new soliton solutions of a fractional Jaulent soliton Miodek system via symmetry analysis are presented in New Soliton Solutions of Fractional Jaulent-Miodek System with Symmetry Analysis

Sub-grid effects of the Voigt viscoelastic regularization of a singular dyadic model of turbulence

In this work we investigate the spectral signature of Navier–Stokes–Voigt (NSV) viscoelastic fluid flows by employing numerical simulations of a singular dyadic shell model. Our results clearly show that as the relaxation time is increased above a threshold, the inertial range is reduced, conserving part of the large-scale statistics. These results differ drastically from the two power-law scenarios observed in a previous work, where the NSV model was studied via Sabra shell model simulations instead. We also show that the additional elastic term regularizes the singular dyadic model, which is the main reason behind this reduction of degrees of freedom. The results of this work aim at proposing the NSV regularization as a sub-grid model.Indisponível